You need more light and a good understanding of contrast ratio.
Imagine you want a 1/1000 shutter. The equation is:
Frame Rate * Shutter Angle = Shutter Speed.
We’re basically stuck at 1/24 for lip synch. So now it’s a matter of algebra.
1/24 * 1/x = 1/1000
x=42
Shutter angle of 1/42 as a degree that’s about 7 degrees. So very very very thin shutter angle.
If a “normal” exposure is 1/24 *1/2=1/48, then you need 5 times the amount of light to keep the same f/stop.
Make sense?